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Register a new userDoes the boson peak survive in an ultrathin oxide glass?
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Bulk glasses exhibit extra vibrational modes at low energies, known as the boson peak. The microscopic dynamics in nanoscale alumina impact the performance of qubits and other superconducting devices, however the existence of the boson peak in these glasses has not been previously measured. Here we report neutron spectroscopy on Al/Al$_2$O$_{3-x}$ nanoparticles consisting of spherical metallic cores from 20 to 1000 nm surrounded by a 3.5 nm thick alumina glass. An intense low-energy peak is observed at $omega_{BP}$ = 2.8 $pm$ 0.6 meV for highly oxidised particles, concurrent with an excess in the density of states. The intensity of the peak scales inversely with particle size and oxide fraction indicating a surface origin, and is red-shifted by 3 meV with respect to the van-Hove singularity of $gamma$-phase Al$_2$O$_{3-x}$ nanocrystals. Molecular dynamics simulations of $alpha$-Al$_2$O$_{3-x}$, $gamma$-Al$_2$O$_{3-x}$ and a-Al$_2$O$_{3-x}$ show that the observed boson peak is a signature of the ultrathin glass surface, and the frequency is softened compared to that of the hypothetical bulk glass.
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We compute the dielectric response of glasses starting from a microscopic system-bath Hamiltonian of the Zwanzig-Caldeira-Leggett type and using an ansatz from kinetic theory for the memory function in the resulting Generalized Langevin Equation. The resulting framework requires the knowledge of the vibrational density of states (DOS) as input, that we take from numerical evaluation of a marginally-stable harmonic disordered lattice, featuring a strong boson peak (excess of soft modes over Debye $simomega_{p}^{2}$ law). The dielectric function calculated based on this ansatz is compared with experimental data for the paradigmatic case of glycerol at $Tlesssim T_{g}$. Good agreement is found for both the reactive (real part) of the response and for the $alpha$-relaxation peak in the imaginary part, with a significant improvement over earlier theoretical approaches, especially in the reactive modulus. On the low-frequency side of the $alpha$-peak, the fitting supports the presence of $sim omega_{p}^{4}$ modes at vanishing eigenfrequency as recently shown in [Phys. Rev. Lett. 117, 035501 (2016)]. $alpha$-wing asymmetry and stretched-exponential behaviour are recovered by our framework, which shows that these features are, to a large extent, caused by the soft boson-peak modes in the DOS.
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